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Statistics · Hypothesis testing

One-Sample t-Test Calculator

Test a population-mean claim from a sample mean, sample standard deviation, and sample size.

Statistics · Hypothesis testing

Enter your statistical inputs

Private in-browser calculation · explicit assumptions
A test statistic is located on its null reference distribution. The selected tail rule defines results at least as extreme.
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
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Enter plain numbers without measurement units. Datasets accept commas, spaces, semicolons, or line breaks and are limited to 10,000 values. Results stay in this browser.

Statistics result

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Understand the hypothesis test

Read the test as a model-based comparison

One-Sample t-Test. The observed effect is scaled by its null-model uncertainty and located on a reference distribution selected before looking at the result.

Test statistic and reference model

t=(x̄−μ₀)/(s/√n), df=n−1.

Report the estimated difference and confidence interval alongside the p-value.

Responsible interpretation

A p-value is not the probability that the null is true, the chance the result occurred ‘by luck,’ or a measure of effect size, importance, replication, bias, or causation.

Required assumption: Observations should be independent and the mean’s t model should be appropriate; significance does not establish practical importance.

Quick guide

How to use this calculator

  1. Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
  2. Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
  3. Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.

Calculation method

How the one-sample t-test calculator works

t=(x̄−μ₀)/(s/√n), df=n−1.

Report the estimated difference and confidence interval alongside the p-value.

Worked example

One-Sample t-Test example

x̄=52, μ₀=50, s=5, n=25 gives t=2.

t=(x̄−μ₀)/(s/√n), df=n−1.

Supported inputs

Precision and limits

Model and design

Observations should be independent and the mean’s t model should be appropriate; significance does not establish practical importance.

Numerical scope

Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.

Interpretation

Report the estimated difference and confidence interval alongside the p-value.

Decision boundary

The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.

Privacy

Entered values and calculated results stay in this browser and are not sent to an analytics service.

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